Fast Inactivation in Shaker K+ Channels : Properties of Ionic and Gating Currents

Fast inactivating Shaker H4 potassium channels and nonconducting pore mutant Shaker H4 W434F channels have been used to correlate the installation and recovery of the fast inactivation of ionic current with changes in the kinetics of gating current known as “charge immobilization” (Armstrong, C.M., and F. Bezanilla. 1977. J. Gen. Physiol. 70:567–590.). Shaker H4 W434F gating currents are very similar to those of the conducting clone recorded in potassium-free solutions. This mutant channel allows the recording of the total gating charge return, even when returning from potentials that would largely inactivate conducting channels. As the depolarizing potential increased, the OFF gating currents decay phase at −90 mV return potential changed from a single fast component to at least two components, the slower requiring ∼200 ms for a full charge return. The charge immobilization onset and the ionic current decay have an identical time course. The recoveries of gating current (Shaker H4 W434F) and ionic current (Shaker H4) in 2 mM external potassium have at least two components. Both recoveries are similar at −120 and −90 mV. In contrast, at higher potentials (−70 and −50 mV), the gating charge recovers significantly more slowly than the ionic current. A model with a single inactivated state cannot account for all our data, which strongly support the existence of “parallel” inactivated states. In this model, a fraction of the charge can be recovered upon repolarization while the channel pore is occupied by the NH₂-terminus region.     

Single-Channel Properties of IKs Potassium Channels

Expressed in Xenopus oocytes, KvLQT1 channel subunits yield a small, rapidly activating, voltage- dependent potassium conductance. When coexpressed with the minK gene product, a slowly activating and much larger potassium current results. Using fluctuation analysis and single-channel recordings, we have studied the currents formed by human KvLQT1 subunits alone and in conjunction with human or rat minK subunits. With low external K⁺, the single-channel conductances of these three channel types are estimated to be 0.7, 4.5, and 6.5 pS, respectively, based on noise analysis at 20 kHz bandwidth of currents at +50 mV. Power spectra computed over the range 0.1 Hz–20 kHz show a weak frequency dependence, consistent with current interruptions occurring on a broad range of time scales. The broad spectrum causes the apparent single-channel current value to depend on the bandwidth of the recording, and is mirrored in very “flickery” single-channel events of the channels from coexpressed KvLQT1 and human minK subunits. The increase in macroscopic current due to the presence of the minK subunit is accounted for by the increased apparent single-channel conductance it confers on the expressed channels. The rat minK subunit also confers the property that the outward single-channel current is increased by external potassium ions.     

Fast and slow gating are inherent properties of the pore module of the K+ channel Kcv

Kcv from the chlorella virus PBCV-1 is a viral protein that forms a tetrameric, functional K⁺ channel in heterologous systems. Kcv can serve as a model system to study and manipulate basic properties of the K⁺ channel pore because its minimalistic structure (94 amino acids) produces basic features of ion channels, such as selectivity, gating, and sensitivity to blockers. We present a characterization of Kcv properties at the single-channel level. In symmetric 100 mM K⁺, single-channel conductance is 114 ± 11 pS. Two different voltage-dependent mechanisms are responsible for the gating of Kcv. “Fast” gating, analyzed by β distributions, is responsible for the negative slope conductance in the single-channel current–voltage curve at extreme potentials, like in MaxiK potassium channels, and can be explained by depletion-aggravated instability of the filter region. The presence of a “slow” gating is revealed by the very low (in the order of 1–4%) mean open probability that is voltage dependent and underlies the time-dependent component of the macroscopic current.     

Idiosyncratic Gating of HERG-like K+ Channels in Microglia

A simple kinetic model is presented to explain the gating of a HERG-like voltage-gated K⁺ conductance described in the accompanying paper (Zhou, W., F.S. Cayabyab, P.S. Pennefather, L.C. Schlichter, and T.E. DeCoursey. 1998. J. Gen. Physiol. 111:781–794). The model proposes two kinetically distinct closing pathways, a rapid one favored by depolarization (deactivation) and a slow one favored by hyperpolarization (inactivation). The overlap of these two processes leads to a window current between −50 and +20 mV with a peak at −36 mV of ∼12% maximal conductance. The near absence of depolarization-activated outward current in microglia, compared with HERG channels expressed in oocytes or cardiac myocytes, can be explained if activation is shifted negatively in microglia. As seen with experimental data, availability predicted by the model was more steeply voltage dependent, and the midpoint more positive when determined by making the holding potential progressively more positive at intervals of 20 s (starting at −120 mV), rather than progressively more negative (starting at 40 mV). In the model, this hysteresis was generated by postulating slow and ultra-slow components of inactivation. The ultra-slow component takes minutes to equilibrate at −40 mV but is steeply voltage dependent, leading to protocol-dependent modulation of the HERG-like current. The data suggest that “deactivation” and “inactivation” are coupled through the open state. This is particularly evident in isotonic Cs⁺, where a delayed and transient outward current develops on depolarization with a decay time constant more voltage dependent and slower than the deactivation process observed at the same potential after a brief hyperpolarization.     

A Combined “Omics” Approach Identifies N-Myc Interactor as a Novel Cytokine-induced Regulator of IRE1α Protein and c-Jun N-terminal Kinase in Pancreatic Beta Cells

Type 1 diabetes is an autoimmune disease with a strong inflammatory component. The cytokines interleukin-1β and interferon-γ contribute to beta cell apoptosis in type 1 diabetes. These cytokines induce endoplasmic reticulum stress and the unfolded protein response (UPR), contributing to the loss of beta cells. IRE1α, one of the UPR mediators, triggers insulin degradation and inflammation in beta cells and is critical for the transition from “physiological” to “pathological” UPR. The mechanisms regulating inositol-requiring protein 1α (IRE1α) activation and its signaling for beta cell “adaptation,” “stress response,” or “apoptosis” remain to be clarified. To address these questions, we combined mammalian protein-protein interaction trap-based IRE1α interactome and functional genomic analysis of human and rodent beta cells exposed to pro-inflammatory cytokines to identify novel cytokine-induced regulators of IRE1α. Based on this approach, we identified N-Myc interactor (NMI) as an IRE1α-interacting/modulator protein in rodent and human pancreatic beta cells. An increased expression of NMI was detected in islets from nonobese diabetic mice with insulitis and in rodent or human beta cells exposed in vitro to the pro-inflammatory cytokines interleukin-1β and interferon-γ. Detailed mechanistic studies demonstrated that NMI negatively modulates IRE1α-dependent activation of JNK and apoptosis in rodent and human pancreatic beta cells. In conclusion, by using a combined omics approach, we identified NMI induction as a novel negative feedback mechanism that decreases IRE1α-dependent activation of JNK and apoptosis in cytokine-exposed beta cells.     

Historical biogeography of the genus Rhadinaea (Squamata: Dipsadinae)

Multiple geological and climatic events have created geographical or ecological barriers associated with speciation events, playing a role in biological diversification in North and Central America. Here, we evaluate the influence of the Neogene and Quaternary geological events, as well as the climatic changes in the diversification of the colubrid snake genus Rhadinaea using molecular dating and ancestral area reconstruction. A multilocus sequence dataset was generated for 37 individuals of Rhadinaea from most of the biogeographical provinces where the genus is distributed, representing 19 of the 21 currently recognized species, and two undescribed species. Our analyses show that the majority of the Rhadinaea species nest in two main clades, herein identified as “Eastern” and “Southern”. These clades probably diverged from each other in the early Miocene, and their divergence was followed by 11 divergences during the middle to late Miocene, three divergences during the Pliocene, and six divergences in the Pleistocene. The ancestral distribution of Rhadinaea was reconstructed across the Sierra Madre del Sur. Our phylogenetic analyses do not support the monophyly of Rhadinaea. The Miocene and Pliocene geomorphology, perhaps in conjunction with climate change, appears to have triggered the diversification of the genus, while the climatic changes during the Miocene probably induced the diversification of Rhadinaea in the Sierra Madre del Sur. Our analysis suggests that the uplifting of the Trans‐Mexican Volcanic Belt and Chiapan–Guatemalan highlands in this same period resulted in northward and southward colonization events. This was followed by more recent, independent colonization events in the Pliocene and Pleistocene involving the Balsas Basin, Chihuahuan Desert, Pacific Coast, Sierra Madre Occidental, Sierra Madre Oriental, Sierra Madre del Sur, Trans‐Mexican Volcanic Belt, and Veracruz provinces, probably driven by the climatic fluctuations of the time.     

Cryo-EM structure of the heptameric calcium homeostasis modulator 1 channel

Calcium homeostasis modulator 1 (CALHM1) is a voltage- and Ca²⁺-gated ATP channel that plays an important role in neuronal signaling. However, as the previously reported CALHM structures are all in the ATP-conducting state, the gating mechanism of ATP permeation is still elusive. Here, we report cryo-EM reconstructions of two Danio rerio CALHM1 heptamers with ordered or flexible long C-terminal helices at resolutions of 3.2 Å and 2.9 Å, respectively, and one D. rerio CALHM1 octamer with flexible long C-terminal helices at a resolution of 3.5 Å. Structural analysis shows that the heptameric CALHM1s are in an ATP-nonconducting state with a central pore diameter of approximately 6.6 Å. Compared with those inside the octameric CALHM1, the N-helix inside the heptameric CALHM1 is in the “down” position to avoid steric clashing with the adjacent TM1 helix. Molecular dynamics simulations show that as the N-helix moves from the “down” position to the “up” position, the pore size of ATP molecule permeation increases significantly. Our results provide important information for elucidating the mechanism of ATP molecule permeation in the CALHM1 channel.     

The Power of Two-Dimensional Dwell-Time Analysis for Model Discrimination, Temporal Resolution, Multichannel Analysis and Level Detection

Two-dimensional (2D) dwell-time analysis of time series of single-channel patch-clamp current was improved by employing a Hinkley detector for jump detection, introducing a genetic fit algorithm, replacing maximum likelihood by a least square criterion, averaging over a field of 9 or 25 bins in the 2D plane and normalizing per measuring time, not per events. Using simulated time series for the generation of the “theoretical” 2D histograms from assumed Markov models enabled the incorporation of the measured filter response and noise. The effects of these improvements were tested with respect to the temporal resolution, accuracy of the determination of the rate constants of the Markov model, sensitivity to noise and requirement of open time and length of the time series. The 2D fit was better than the classical hidden Markov model (HMM) fit in all tested fields. The temporal resolution of the two most efficient algorithms, the 2D fit and the subsequent HMM/beta fit, enabled the determination of rate constants 10 times faster than the corner frequency of the low-pass filter. The 2D fit was much less sensitive to noise. The requirement of computing time is a problem of the 2D fit (100 times that of the HMM fit) but can now be handled by personal computers. The studies revealed a fringe benefit of 2D analysis: it can reveal the “true” single-channel current when the filter has reduced the apparent current level by averaging over undetected fast gating.     

Interference of Shot Noise of Open-Channel Current with Analysis of Fast Gating: Patchers do not (Yet) Have to Care

Microsecond gating of ion channels can be evaluated by fitting beta distributions to amplitude histograms of measured time series. The shape of these histograms is determined not only by the rate constants of the gating process (in relation to the filter frequency) but also by baseline noise and shot noise, resulting from the stochastic nature of ion flow. Under normal temporal resolution, the small shot noise can be ignored. This simplification may no longer be legitimate when rate constants reach the range above 1 μs⁻¹. Here, the influence of shot noise is studied by means of simulated time series for several values of single-channel current of the fully open state and baseline noise. Under realistic optimal conditions (16 pA current, 1 pA noise, 50 kHz bandwidth), ignoring the shot noise leads to an underestimation of the rate constants above 1 μs⁻¹ by a factor of about 2.5. However, in that range, the scatter of the evaluated rate constants is at least of the same magnitude, obscuring the systematic error. The incorporation of shot noise into the analysis will become more important when amplifiers with significantly reduced noise become available.     

Mechanotransduction by Membrane Proteins: The speed of the hair cell mechanotransducer channel revealed by fluctuation analysis

Although mechanoelectrical transducer (MET) channels have been extensively studied, uncertainty persists about their molecular architecture and single-channel conductance. We made electrical measurements from mouse cochlear outer hair cells (OHCs) to reexamine the MET channel conductance comparing two different methods. Analysis of fluctuations in the macroscopic currents showed that the channel conductance in apical OHCs determined from nonstationary noise analysis was about half that of single-channel events recorded after tip link destruction. We hypothesized that this difference reflects a bandwidth limitation in the noise analysis, which we tested by simulations of stochastic fluctuations in modeled channels. Modeling indicated that the unitary conductance depended on the relative values of the channel activation time constant and the applied low-pass filter frequency. The modeling enabled the activation time constant of the channel to be estimated for the first time, yielding a value of only a few microseconds. We found that the channel conductance, assayed with both noise and recording of single-channel events, was reduced by a third in a new deafness mutant, Tmc1 p.D528N. Our results indicate that noise analysis is likely to underestimate MET channel amplitude, which is better characterized from recordings of single-channel events.     

Hydrophobic Gating of Ion Permeation in Magnesium Channel CorA

Ion channels catalyze ionic permeation across membranes via water-filled pores. To understand how changes in intracellular magnesium concentration regulate the influx of Mg²⁺ into cells, we examine early events in the relaxation of Mg²⁺ channel CorA toward its open state using massively-repeated molecular dynamics simulations conducted either with or without regulatory ions. The pore of CorA contains a 2-nm-long hydrophobic bottleneck which remained dehydrated in most simulations. However, rapid hydration or “wetting” events concurrent with small-amplitude fluctuations in pore diameter occurred spontaneously and reversibly. In the absence of regulatory ions, wetting transitions are more likely and include a wet state that is significantly more stable and more hydrated. The free energy profile for Mg²⁺ permeation presents a barrier whose magnitude is anticorrelated to pore diameter and the extent of hydrophobic hydration. These findings support an allosteric mechanism whereby wetting of a hydrophobic gate couples changes in intracellular magnesium concentration to the onset of ionic conduction.     

The “Genetic Program”: Behind the Genesis of an Influential Metaphor

The metaphor of the “genetic program,” indicating the genome as a set of instructions required to build a phenotype, has been very influential in biology despite various criticisms over the years. This metaphor, first published in 1961, is thought to have been invented independently in two different articles, one by Ernst Mayr and the other by François Jacob and Jacques Monod. Here, after a detailed analysis of what both parties meant by “genetic program,” I show, using unpublished archives, the strong resemblance between the ideas of Mayr and Monod and suggest that their idea of genetic program probably shares a common origin. I explore the possibility that the two men met before 1961 and also exchanged their ideas through common friends and colleagues in the field of molecular biology. Based on unpublished correspondence of Jacob and Monod, I highlight the important events that influenced the preparation of their influential paper, which introduced the concept of the genetic program. Finally, I suggest that the genetic program metaphor may have preceded both papers and that it was probably used informally before 1961.     

On the validation of crystallographic symmetry and the quality of structures

In 2008, Zwart and colleagues observed that the fraction of the structures deposited in the PDB alleged to have “pseudosymmetry” or “special noncrystallographic symmetry” (NCS) was about 6%, and that this percentage was rising annually. A few years later, Poon and colleagues found that 2% of all the crystal structures in the PDB belonged to higher symmetry space groups than those assigned to them. Here, I report an analysis of the X-ray diffraction data deposited for this class of structures, which shows that most of the “pseudosymmetry” and “special NCS” that has been reported is in fact true crystallographic symmetry (CS). This distinction is important because the credibility of crystal structures depends heavily on quality control statistics such as R_free that are unreliable when they are computed incorrectly, which they often are when CS is misidentified as “special NCS” or “pseudosymmetry”. When mistakes of this kind are made, artificially low values of R_free can give unjustified confidence in the accuracy of the reported structures.     

Heart Rate and Systolic Blood Pressure Variability in the Time Domain in Patients with Recent and Long-Standing Diabetes Mellitus

Diabetes Mellitus (DM) affects the cardiovascular response of patients. To study this effect, interbeat intervals (IBI) and beat-to-beat systolic blood pressure (SBP) variability of patients during supine, standing and controlled breathing tests were analyzed in the time domain. Simultaneous noninvasive measurements of IBI and SBP for 30 recently diagnosed and 15 long-standing DM patients were compared with the results for 30 rigorously screened healthy subjects (control). A statistically significant distinction between control and diabetic subjects was provided by the standard deviation and the higher moments of the distributions (skewness, and kurtosis) with respect to the median. To compare IBI and SBP for different populations, we define a parameter, α, that combines the variability of the heart rate and the blood pressure, as the ratio of the radius of the moments for IBI and the same radius for SBP. As diabetes evolves, α decreases, standard deviation of the IBI detrended signal diminishes (heart rate signal becomes more “rigid”), skewness with respect to the median approaches zero (signal fluctuations gain symmetry), and kurtosis increases (fluctuations concentrate around the median). Diabetes produces not only a rigid heart rate, but also increases symmetry and has leptokurtic distributions. SBP time series exhibit the most variable behavior for recently diagnosed DM with platykurtic distributions. Under controlled breathing, SBP has symmetric distributions for DM patients, while control subjects have non-zero skewness. This may be due to a progressive decrease of parasympathetic and sympathetic activity to the heart and blood vessels as diabetes evolves.     

Oral and long‐acting antipsychotics for relapse prevention in schizophrenia‐spectrum disorders: a network meta‐analysis of 92 randomized trials including 22,645 participants

According to current evidence and guidelines, continued antipsychotic treatment is key for preventing relapse in people with schizophrenia‐spectrum disorders, but evidence‐based recommendations for the choice of the individual antipsychotic for maintenance treatment are lacking. Although oral antipsychotics are often prescribed first line for practical reasons, long‐acting injectable antipsychotics (LAIs) are a valuable resource to tackle adherence issues since the earliest phase of disease. Medline, EMBASE, PsycINFO, CENTRAL and CINAHL databases and online registers were searched to identify randomized controlled trials comparing LAIs or oral antipsychotics head‐to‐head or against placebo, published until June 2021. Relative risks and standardized mean differences were pooled using random‐effects pairwise and network meta‐analysis. The primary outcomes were relapse and dropout due to adverse events. We used the Cochrane Risk of Bias tool to assess study quality, and the CINeMA approach to assess the confidence of pooled estimates. Of 100 eligible trials, 92 (N=22,645) provided usable data for meta‐analyses. Regarding relapse prevention, the vast majority of the 31 included treatments outperformed placebo. Compared to placebo, “high” confidence in the results was found for (in descending order of effect magnitude) amisulpride‐oral (OS), olanzapine‐OS, aripiprazole‐LAI, olanzapine‐LAI, aripiprazole‐OS, paliperidone‐OS, and ziprasidone‐OS. “Moderate” confidence in the results was found for paliperidone‐LAI 1‐monthly, iloperidone‐OS, fluphenazine‐OS, brexpiprazole‐OS, paliperidone‐LAI 1‐monthly, asenapine‐OS, haloperidol‐OS, quetiapine‐OS, cariprazine‐OS, and lurasidone‐OS. Regarding tolerability, none of the antipsychotics was significantly worse than placebo, but confidence was poor, with only aripiprazole (both LAI and OS) showing “moderate” confidence levels. Based on these findings, olanzapine, aripiprazole and paliperidone are the best choices for the maintenance treatment of schizophrenia‐spectrum disorders, considering that both LAI and oral formulations of these antipsychotics are among the best‐performing treatments and have the highest confidence of evidence for relapse prevention. This finding is of particular relevance for low‐ and middle‐income countries and constrained‐resource settings, where few medications may be selected. Results from this network meta‐analysis can inform clinical guidelines and national and international drug regulation policies.     

Detection of copy number variations and their effects in Chinese bulls

Background

Copy number variations (CNVs) are a main source of genomic structural variations underlying animal evolution and production traits. Here, with one pure-blooded Angus bull as reference, we describe a genome-wide analysis of CNVs based on comparative genomic hybridization arrays in 29 Chinese domesticated bulls and examined their effects on gene expression and cattle growth traits.

Results

We identified 486 copy number variable regions (CNVRs), covering 2.45% of the bovine genome, in 24 taurine (Bos taurus), together with 161 ones in 2 yaks (Bos grunniens) and 163 ones in 3 buffaloes (Bubalus bubalis). Totally, we discovered 605 integrated CNVRs, with more “loss” events than both “gain” and “both” ones, and clearly clustered them into three cattle groups. Interestingly, we confirmed their uneven distributions across chromosomes, and the differences of mitochondrion DNA copy number (gain: taurine, loss: yak & buffalo). Furthermore, we confirmed approximately 41.8% (253/605) and 70.6% (427/605) CNVRs span cattle genes and quantitative trait loci (QTLs), respectively. Finally, we confirmed 6 CNVRs in 9 chosen ones by using quantitative PCR, and further demonstrated that CNVR22 had significantly negative effects on expression of PLA2G2D gene, and both CNVR22 and CNVR310 were associated with body measurements in Chinese cattle, suggesting their key effects on gene expression and cattle traits.

Conclusions

The results advanced our understanding of CNV as an important genomic structural variation in taurine, yak and buffalo. This study provides a highly valuable resource for Chinese cattle’s evolution and breeding researches.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-480) contains supplementary material, which is available to authorized users.     

Functional Properties of the Retinal Glutamate Transporters GLT-1c and EAAT5

In the mammalian retina, glutamate uptake is mediated by members of a family of glutamate transporters known as “excitatory amino acid transporters (EAATs).” Here we cloned and functionally characterized two retinal EAATs from mouse, the GLT-1/EAAT2 splice variant GLT-1c, and EAAT5. EAATs are glutamate transporters and anion-selective ion channels, and we used heterologous expression in mammalian cells, patch-clamp recordings and noise analysis to study and compare glutamate transport and anion channel properties of both EAAT isoforms. We found GLT-1c to be an effective glutamate transporter with high affinity for Na⁺ and glutamate that resembles original GLT-1/EAAT2 in all tested functional aspects. EAAT5 exhibits glutamate transport rates too low to be accurately measured in our experimental system, with significantly lower affinities for Na⁺ and glutamate than GLT-1c. Non-stationary noise analysis demonstrated that GLT-1c and EAAT5 also differ in single-channel current amplitudes of associated anion channels. Unitary current amplitudes of EAAT5 anion channels turned out to be approximately twice as high as single-channel amplitudes of GLT-1c. Moreover, at negative potentials open probabilities of EAAT5 anion channels were much larger than for GLT-1c. Our data illustrate unique functional properties of EAAT5, being a low-affinity and low-capacity glutamate transport system, with an anion channel optimized for anion conduction in the negative voltage range.     

A residue at the cytoplasmic entrance of BK-type channels regulating single-channel opening by its hydrophobicity

Single large-conductance calcium-activated K⁺ (BK) channels encoded by the mSlo gene usually have synchronous gating, but a Drosophila dSlo (A2/C2/E2/G5/10) splice variant (dSlo1A) exhibits very flickery openings. To probe this difference in gating, we constructed a mutant I323T. This channel exhibits four subconductance levels similar to those of dSlo1A. Rectification of the single-channel current-voltage relation of I323T decreased as [Ca²⁺ ]_in increased from 10 to 300 μM. Mutagenesis suggests that the hydrophobicity of the residue at the position is important for the wild-type gating; i.e., increasing hydrophobicity prolongs open duration. Molecular dynamics simulation suggests that four hydrophobic pore-lining residues at position 323 of mSlo act cooperatively in a “shutter-like” mechanism gating the permeation of K⁺ ions. Rate-equilibrium free energy relations analysis shows that the four I323 residues in an mSlo channel have a conformation 65% similar to the closed conformation during gating. Based on these observations, we suggest that the appearance of rectification and substates of BK-type channels arise from a reduction of the cooperativity among these four residues and a lower probability of being open.     

Gating Kinetics of Single Large-Conductance Ca2+-Activated K+ Channels in High Ca2+ Suggest a Two-Tiered Allosteric Gating Mechanism?

The Ca²⁺-dependent gating mechanism of large-conductance calcium-activated K⁺ (BK) channels from cultured rat skeletal muscle was examined from low (4 μM) to high (1,024 μM) intracellular concentrations of calcium (Ca²⁺ _i) using single-channel recording. Open probability (P _o) increased with increasing Ca²⁺ _i (K _0.5 11.2 ± 0.3 μM at +30 mV, Hill coefficient of 3.5 ± 0.3), reaching a maximum of ∼0.97 for Ca²⁺ _i ∼ 100 μM. Increasing Ca²⁺ _i further to 1,024 μM had little additional effect on either P _o or the single-channel kinetics. The channels gated among at least three to four open and four to five closed states at high levels of Ca²⁺ _i (>100 μM), compared with three to four open and five to seven closed states at lower Ca²⁺ _i. The ability of kinetic schemes to account for the single-channel kinetics was examined with simultaneous maximum likelihood fitting of two-dimensional (2-D) dwell-time distributions obtained from low to high Ca²⁺ _i. Kinetic schemes drawn from the 10-state Monod-Wyman-Changeux model could not describe the dwell-time distributions from low to high Ca²⁺ _i. Kinetic schemes drawn from Eigen''s general model for a ligand-activated tetrameric protein could approximate the dwell-time distributions but not the dependency (correlations) between adjacent intervals at high Ca²⁺ _i. However, models drawn from a general 50 state two-tiered scheme, in which there were 25 closed states on the upper tier and 25 open states on the lower tier, could approximate both the dwell-time distributions and the dependency from low to high Ca²⁺ _i. In the two-tiered model, the BK channel can open directly from each closed state, and a minimum of five open and five closed states are available for gating at any given Ca²⁺ _i. A model that assumed that the apparent Ca²⁺-binding steps can reach a maximum rate at high Ca²⁺ _i could also approximate the gating from low to high Ca²⁺ _i. The considered models can serve as working hypotheses for the gating of BK channels.